diff -r f04b33ce250f -r a4dc62a46ee4 ex/Acc.ML --- a/ex/Acc.ML Tue Oct 24 14:59:17 1995 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,63 +0,0 @@ -(* Title: HOL/ex/Acc - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1994 University of Cambridge - -Inductive definition of acc(r) - -See Ch. Paulin-Mohring, Inductive Definitions in the System Coq. -Research Report 92-49, LIP, ENS Lyon. Dec 1992. -*) - -open Acc; - -(*The intended introduction rule*) -val prems = goal Acc.thy - "[| !!b. :r ==> b: acc(r) |] ==> a: acc(r)"; -by (fast_tac (set_cs addIs (prems @ - map (rewrite_rule [pred_def]) acc.intrs)) 1); -qed "accI"; - -goal Acc.thy "!!a b r. [| b: acc(r); : r |] ==> a: acc(r)"; -by (etac acc.elim 1); -by (rewtac pred_def); -by (fast_tac set_cs 1); -qed "acc_downward"; - -val [major,indhyp] = goal Acc.thy - "[| a : acc(r); \ -\ !!x. [| x: acc(r); ALL y. :r --> P(y) |] ==> P(x) \ -\ |] ==> P(a)"; -by (rtac (major RS acc.induct) 1); -by (rtac indhyp 1); -by (resolve_tac acc.intrs 1); -by (rewtac pred_def); -by (fast_tac set_cs 2); -by (etac (Int_lower1 RS Pow_mono RS subsetD) 1); -qed "acc_induct"; - - -val [major] = goal Acc.thy "r <= Sigma(acc(r), %u. acc(r)) ==> wf(r)"; -by (rtac (major RS wfI) 1); -by (etac acc.induct 1); -by (rewtac pred_def); -by (fast_tac set_cs 1); -qed "acc_wfI"; - -val [major] = goal Acc.thy "wf(r) ==> ALL x. : r | :r --> y: acc(r)"; -by (rtac (major RS wf_induct) 1); -by (rtac (impI RS allI) 1); -by (rtac accI 1); -by (fast_tac set_cs 1); -qed "acc_wfD_lemma"; - -val [major] = goal Acc.thy "wf(r) ==> r <= Sigma(acc(r), %u. acc(r))"; -by (rtac subsetI 1); -by (res_inst_tac [("p", "x")] PairE 1); -by (fast_tac (set_cs addSIs [SigmaI, - major RS acc_wfD_lemma RS spec RS mp]) 1); -qed "acc_wfD"; - -goal Acc.thy "wf(r) = (r <= Sigma(acc(r), %u. acc(r)))"; -by (EVERY1 [rtac iffI, etac acc_wfD, etac acc_wfI]); -qed "wf_acc_iff";